Summary Mental and neuropsychiatric illnesses (including depression, Alzheimer's Disease, and many others) will affect roughly 20% of the population sometime during their lifetimes. By some measurements these illnesses represent the leading category of disease burden worldwide. Positron Emission Tomography (PET) of the brain has become an invaluable research tool for studying such illnesses because it allows quanti?cation of the density of various molecules throughout the brain. In the current state of the art in the analysis of PET imaging data, there are two major drawbacks. The ?rst is that analysis is always done as a ?two-stage? process: Stage 1 consists of modeling the PET data over time to get a single (scalar) estimate of receptor density, either for each voxel or for each of one or more regions of interest. Subsequently, in Stage 2 these estimates are effectively regarded as the observed data, and statistical analysis involves comparing these estimates across individuals, between diagnostic groups, etc. This is an inef?cient use of data and it does not allow good precision when investigating some subtle systematic effects. The second major drawback is that the ?eld relies almost exclusively on parametric models. The basic model for PET data in a voxel or ROI is a kinetic model that relies on some fairly strong assumptions about the biological processes that, while they are often reasonable approximations to the truth in some instances, are often thought to be violated. By relying on principles of functional data analysis (FDA), we can open up a powerful new analysis structure for investigating differences among individuals, among groups, and for making individual- level predictions (e.g., response to treatment). This project will undertake the following three aims. 1. To develop methodology based on parametric models that combines both Stage 1 and Stage 2 into a single analysis process. This will allow for much more re?ned analysis that can look for differences between groups in individual kinetic rate parameters, rather than relying only on aggregate outcome measures. 2. To develop FDA-based tools for comparing PET imaging data across subjects, across groups, etc. This will require new analysis methods since the relevant functional data are not observed directly but can only be estimated using some form of nonparametric deconvolution algorithm of the observed PET data over time. 3. To incorporate recent advances made by our group and others, in the contexts of both the parametric and the nonparametric approaches, to the situation in which blood data and/or a ?reference region? is not available. Aim 1 is intended for PET radiotracers in which parametric models exist and provide a reasonable ?t for the data. Aim 2 is intended both for tracers not described well by usual parametric models and also as supplementary nonparametric analysis. Aim 3 will extend the reach of these methods and widen the potential application of PET imaging. These new advances have the potential to greatly enhance our understanding of the biological underpinnings of many neuropsychiatric diseases as well as response to treatment.